View Single Post
2005-04-30, 23:28   #1
PBMcL

Jan 2005

2·31 Posts
64-bit GMP-ECM on Apple G5/OS X v10.4

Apple's just-released OS X v10.4 supports true 64-bit computing on its G5 (PowerPC970) models. The attached G5_64bit_GMP-ECM.zip archive contains all of the instructions, patches, and extra files you'll need to build and install 64-bit versions of GMP-4.1.4 and ECM-6.0.1 on a G5.

The improvement over 32-bit code is fairly dramatic; here are timing comparisons for some Cunningham cofactors (6^329 - 1, 2^833 + 1, 5^421 + 1, 2^ 2018 + 1, and 10^386 + 1) of various lengths:

32-bit version of GMP-ECM on Apple G5, 2.5 GHz, OS X 10.3.8:

Input number is 65030090232295456717...09355134587611097719 (150 digits)
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=513591587
Step 1 took 70190ms
Step 2 took 29210ms
Input number is 11846804646723081354...15329989531005685163 (200 digits)
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=3742068876
Step 1 took 88700ms
Step 2 took 41500ms
Input number is 74153397868455467120...13316867740036509963 (250 digits)
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=1201248243
Step 1 took 155260ms
Step 2 took 50580ms
Input number is 45306169533352784567...10063050866528133509 (300 digits)
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=3821960013
Step 1 took 228200ms
Step 2 took 64230ms
Input number is 68760637088087042795...66376993609358157449 (348 digits)
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=3555916332
Step 1 took 293210ms
Step 2 took 81590ms

64-bit version of GMP-ECM on Apple G5, 2.5 GHz, OS X 10.4:

Input number is 65030090232295456717...09355134587611097719 (150 digits)
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=861374654
Step 1 took 30948ms
Step 2 took 16502ms
Input number is 11846804646723081354...15329989531005685163 (200 digits)
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=3093777225
Step 1 took 40605ms
Step 2 took 22657ms
Input number is 74153397868455467120...13316867740036509963 (250 digits)
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=2753020307
Step 1 took 63725ms
Step 2 took 27288ms
Input number is 45306169533352784567...10063050866528133509 (300 digits)
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=4290308355
Step 1 took 90626ms
Step 2 took 35623ms
Input number is 68760637088087042795...66376993609358157449 (348 digits)
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=366885523
Step 1 took 120730ms
Step 2 took 43114ms

Post here or contact me if you have any problems.

Phil McLaughlin
Attached Files
 G5_64bit_GMP-ECM.zip (22.6 KB, 178 views)